Generalized entropy index

The generalized or generalized entropy, respectively, the generalized / generalized entropy index ( abbreviation: GE) is a general formula for redundancy measurement ( data ). The redundancy can be considered as disparity ( inequality), lack of diversity, non- randomness, compressibility or segregation of the data. Mainly found this measure as Ungleichverteilungsmaß application. It is similar to the definition of redundancy, which is based on the Shannon entropy, if, which is referred to in the inequality measurement as Theil index. These are completely different data have no redundancy, so it follows that it. In the opposite direction of a Disparitätsmaßes This takes in order rather than messing up, so it is a negated measure of entropy.

Formula

The formula is:

Where the income of each individual, which means a part of and is the weighting of the distances between incomes at different parts of the income distribution is. Sometimes is used in a different notation.

For lower values ​​of close to 0, the GE is sensitive at lower income levels and vice versa ( reverse) for values ​​of almost 1 is at the front and the Theil- L index, the mean logarithmic deviation, at. If it is, the value is half of the square root of the coefficient of variation:

The GE is a transformation of the Atkinson measure, which applies. This transformation is such that the Atkinson measure a probability rather than an entropy.

If by by ( for example: income per person is changing to person depending on income ) is replaced, then with equivalent.